Will my new job honor my vaccine exemption?

I'm currently employed by the federal government, and I'm moving to a new department at the start of next year. My current department granted me an exemption to the vaccine on religious grounds, but I'm concerned that the new department won't honor that. In a way, I don't see why they wouldn't since government agencies all have to follow the same guidelines/rules. Is there a chance my exemption carries over?

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